Abstract

Evaluating the Underreserving Risk in the Framework of Chain-ladder-Methods by the Help of Monte-Carlo Simulation

Magda Schiegl

Versicherungskammer Bayern

A method for analysing underreserving risk in the framework of integrated risk management is developed through combination of chain - ladder - method and mean square error (m.s.e.) concept with Monte Carlo simulation of run off tables. An analytic expression for chain - ladder - reserve's m.s.e. was derived in the literature [1]. For simulating run-off tables we use the collective model: Claim numbers are assumed to be Poisson-, claim sizes Pareto-distributed. Our method can be also applied to other distributions. We analyse the deviance between chain - ladder reserves and Monte Carlo simulated reserves statistically. Results document the relevance of m.s.e. as a reserving risk measure. Dependencies on claim size and claim number distribution's parameters are observed. For practical use a technique is developed that quantifies the risk of underreservation and enables its reduction to a given level by taking an additional reserve proportional to m.s.e. In insurance companies for most lines of business data for a reliable estimation of claim size and claim number distribution parameters are available. Chain-ladder-methods are used for reserving, pricing and asset-liability-management.